4 men or 12 boys can do a certain work in 36 days. How long will 6 men and 10 boys take to do it?

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.

kherson [118]

Answer:

Completing the square.

Step-by-step explanation:

ax2 + bx + c has "x" in it twice, which is hard to solve.

But there is a way to rearrange it so that "x" only appears once. It is called Completing the Square

3 0

2 years ago

I'm thinking of a ten-digit integer whose digits are all distinct. It happens that the number formed by the first n of them is d

omeli [17]

The problem here takes a brilliant mind to answer this. This problem can easily be answered using programming because we can not then and there push all the possibilities using paper and pen.

The answer is 3816547290.

Trying all the possibilities starting form 1000000080 (we are sure that the last number should be 0). Then traversing that number until 9999999990. Each traverse, check the number if its divisible to n, so on and so forth.

6 0

3 years ago

28 cm 45 cm What is the length of the hypotenuse?

maksim [4K]

Answer:

53 cm

Step-by-step explanation:

Using Pythagoras Theorem,

The hypotenuse

$= \sqrt{ {28}^{2} + {45}^{2} }$

$= \sqrt{2809}$

= 53 cm

8 0

3 years ago

Read 2 more answers

Which pair of expressions is equivalent using the Associative Property of Multiplication?

RUDIKE [14]

Answer:

Step-by-step explanation:

In the associative property of multiplication, the product of the multiplication of 3 or more numbers is the same irrespective of how they are grouped. This means that irrespective of the bracket or which number comes first, the product will always be the same.

From the given scenarios, the pair of expressions that are equivalent using the Associative Property of Multiplication are

B 6(4a ⋅ 2) = (4a ⋅ 2) ⋅ 6

C 6(4a ⋅ 2) = 6 ⋅ 4a ⋅ 2

D6(4a ⋅ 2) = (6 ⋅ 4a) ⋅ 2

The results are the same irrespective of the arrangement of the numbers.

3 0

3 years ago

Find the length of the following two-dimensional curve. r (t ) = (1/2 t^2, 1/3(2t+1)^3/2) for 0 < t < 16

andrezito [222]

Answer:

r = 144 units

Step-by-step explanation:

The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;

$r(t)=\int\limits^a_b ({r`)^2 \, dt =\int\limits^b_a \sqrt{((\frac{dx}{dt} )^2 +\frac{dy}{dt} )^2)} dt$

In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.

Substituting the terms of the equation and the derivative of r´, as follows,

$r(t)= \int\limits^b_a \sqrt{((\frac{d((1/2)t^2)}{dt} )^2 +\frac{d((1/3)(2t+1)^{3/2})}{dt} )^2)} dt$